On bending consistency of Timoshenko beam using differential and integral nonlocal strain gradient models,ZAMM - Journal of Applied Mathematics and Mechanics

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On bending consistency of Timoshenko beam using differential and integral nonlocal strain gradient models
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2021-02-01 , DOI: 10.1002/zamm.202000132
Pei‐Liang Bian ₁ , Hai Qing ₁

Affiliation

In this work, the static bending response of Timoshenko beam under different boundary and loading conditions is analyzed and compared with the application of nonlocal strain gradient models in differential (DNSGM) and integral (INSGM) forms. High-order and standard boundary conditions are introduced for DNSGM, while the relation between strain and nonlocal stress are expressed as integral equations for INSGM. The differential equations for DNSGM and integro-differential equations for INSGM are solved directly with the Laplace transformation. The explicit expression for bending deflection and rotation is derived uniquely with eight unknown constants for both DNSGM and INSGM. The results obtained with current models are validated against to the existing results in literature. On the static bending of Timoshenko beam subjected to different boundary and loading conditions, inconsistent responses occurs for DNSGM, while consistent softening and toughening responses can be obtained for INSGM.

中文翻译：

使用微分和积分非局部应变梯度模型研究 Timoshenko 梁的弯曲一致性

在这项工作中，铁木辛哥梁在不同边界和加载条件下的静态弯曲响应进行了分析，并与微分（DNSGM）和积分（INSGM）形式的非局部应变梯度模型的应用进行了比较。DNSGM 引入了高阶边界条件和标准边界条件，而应变与非局部应力之间的关系用 INSGM 的积分方程表示。DNSGM 的微分方程和 INSGM 的积分微分方程直接用拉普拉斯变换求解。弯曲挠度和旋转的显式表达式是通过 DNSGM 和 INSGM 的八个未知常数唯一导出的。使用当前模型获得的结果与文献中的现有结果进行了验证。

更新日期：2021-02-01

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